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Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids

Charlotte Gils; Simon Trebst; Alexei Kitaev; Andreas W. W. Ludwig; Matthias Troyer; Zhenghan Wang · Nature Physics · 2009 · Analytical and numerical theory of interacting anyons

Original publication · Original publication

Recorded summary

An interacting-anyon model connects topological quantum phases through topology-driven transitions. Fibonacci-anyon theory provides a concrete setting, including an exactly solvable linear geometry.

Recorded limitations

This is theoretical work rather than a device demonstration. Applicability to a physical implementation requires separate evidence; the present review uses the abstract and accessible figure descriptions.

Evidence and provenance

Chapter Trust Factor uses a minimum of three distinct qualifying studies. Publication records retain their own evidence and assessment.

Study design and assessment
design
Analytical and numerical theory of interacting anyons
assessment
is Randomized Controlled Trial
false
blinding
Not applicable to a clinical-trial grade
basis
Analytical and numerical theory of interacting anyons. No human randomized controlled trial is reported.
sources

https://www.nature.com/articles/nphys1396

category
peer-reviewed
peer Reviewed
true
trust Factor
score
1
scope
Paper
status
assessed
randomized Controlled Trial
false
blinding
not-confirmed
peer Reviewed
true
basis
Analytical and numerical theory of interacting anyons. No human randomized controlled trial is reported.
sources

https://www.nature.com/articles/nphys1396

review Scope
Existing publication-specific assessments and bibliographic indexing; no blanket full-text appraisal.
assessed At
2026-10-27
jadad
status
not-applicable
score
Not recorded
reason
Not a human randomized controlled trial.
evidence
evidence Type
Analytical and numerical theory of interacting anyons
evidence Class
mathematical_computational_model
measurement
Microscopic anyon model; exact solution and numerical spectra
measured Genes
None recorded
pathways
None recorded
relationship Note
Background literature only. This paper does not test or validate an OXTR–Fibonacci relationship.
clinical Evidence
false
review Depth
Abstract and selected source passages: Abstract; Figure 3, The Fibonacci theory; publisher metadata.
full Paper Appraisal
Not completed; review depth states the material assessed.
Topics and recorded topic scores
  1. key
    general:fibonacci-quantum-information
    title
    Quantum information and Fibonacci dynamics
    collection
    general
    trust Score
    1
Citation snapshot and identifiers
id
nature-fibonacci-nphys1396
doi
10.1038/nphys1396
pmid
Not recorded
citation Snapshot
count
65
source
Crossref cited-by count
retrieved At
2026-10-24
url
https://api.crossref.org/works/10.1038/nphys1396
field
is-referenced-by-count
source Indexed At
2026-08-05T03:02:50Z
coverage Note
Count reflects Crossref-deposited references and can differ from publisher or other database totals. It is not a quality or clinical-evidence score.
citations By Collection
general
65
Complete approved library record
id
nature-fibonacci-nphys1396
aliases
None recorded
title
Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids
journal
Nature Physics
publisher Family
nature
publisher Family Label
Nature Portfolio
neurotransmitters
None recorded
year
2009
authors
Charlotte Gils; Simon Trebst; Alexei Kitaev; Andreas W. W. Ludwig; Matthias Troyer; Zhenghan Wang
design
Analytical and numerical theory of interacting anyons
kind
Journal article
identity Conflict
Not recorded
doi
10.1038/nphys1396
pmid
Not recorded
urls

https://www.nature.com/articles/nphys1396 · https://doi.org/10.1038/nphys1396

collections

general

categories

Fibonacci mathematics · Quantum information

targets
None recorded
priority
1
quotes
None recorded
summary
An interacting-anyon model connects topological quantum phases through topology-driven transitions. Fibonacci-anyon theory provides a concrete setting, including an exactly solvable linear geometry.
limitation
This is theoretical work rather than a device demonstration. Applicability to a physical implementation requires separate evidence; the present review uses the abstract and accessible figure descriptions.
citation Count
65
citation Snapshot
count
65
source
Crossref cited-by count
retrieved At
2026-10-24
url
https://api.crossref.org/works/10.1038/nphys1396
field
is-referenced-by-count
source Indexed At
2026-08-05T03:02:50Z
coverage Note
Count reflects Crossref-deposited references and can differ from publisher or other database totals. It is not a quality or clinical-evidence score.
study Design Assessment
is Randomized Controlled Trial
false
blinding
Not applicable to a clinical-trial grade
basis
Analytical and numerical theory of interacting anyons. No human randomized controlled trial is reported.
sources

https://www.nature.com/articles/nphys1396

category
peer-reviewed
peer Reviewed
true
paper Trust Assessment
score
1
scope
Paper
status
assessed
randomized Controlled Trial
false
blinding
not-confirmed
peer Reviewed
true
basis
Analytical and numerical theory of interacting anyons. No human randomized controlled trial is reported.
sources

https://www.nature.com/articles/nphys1396

review Scope
Existing publication-specific assessments and bibliographic indexing; no blanket full-text appraisal.
assessed At
2026-10-27
citations By Collection
general
65
topics
  1. key
    general:fibonacci-quantum-information
    title
    Quantum information and Fibonacci dynamics
    collection
    general
    trust Score
    1
journal Key
naturephysics
journal Label
Nature Physics
chapter Entries
  1. id
    general-nature-fibonacci-nphys1396
    title
    Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids
    journal
    Nature Physics
    year
    2009
    authors
    Charlotte Gils; Simon Trebst; Alexei Kitaev; Andreas W. W. Ludwig; Matthias Troyer; Zhenghan Wang
    doi
    10.1038/nphys1396
    pmid
    Not recorded
    urls

    https://www.nature.com/articles/nphys1396 · https://doi.org/10.1038/nphys1396

    design
    Analytical and numerical theory of interacting anyons
    summary
    An interacting-anyon model connects topological quantum phases through topology-driven transitions. Fibonacci-anyon theory provides a concrete setting, including an exactly solvable linear geometry.
    limitation
    This is theoretical work rather than a device demonstration. Applicability to a physical implementation requires separate evidence; the present review uses the abstract and accessible figure descriptions.
    citation Count
    65
    citation Snapshot
    count
    65
    source
    Crossref cited-by count
    retrieved At
    2026-10-24
    url
    https://api.crossref.org/works/10.1038/nphys1396
    field
    is-referenced-by-count
    source Indexed At
    2026-08-05T03:02:50Z
    coverage Note
    Count reflects Crossref-deposited references and can differ from publisher or other database totals. It is not a quality or clinical-evidence score.
    categories

    Fibonacci mathematics · Quantum information

    targets
    None recorded
    evidence
    evidence Type
    Analytical and numerical theory of interacting anyons
    evidence Class
    mathematical_computational_model
    measurement
    Microscopic anyon model; exact solution and numerical spectra
    measured Genes
    None recorded
    pathways
    None recorded
    relationship Note
    Background literature only. This paper does not test or validate an OXTR–Fibonacci relationship.
    clinical Evidence
    false
    review Depth
    Abstract and selected source passages: Abstract; Figure 3, The Fibonacci theory; publisher metadata.
    full Paper Appraisal
    Not completed; review depth states the material assessed.
    record Id
    nature-fibonacci-nphys1396
    quotes
    None recorded
    source Pages
    None recorded
    paper Trust Assessment
    score
    1
    scope
    Paper
    status
    assessed
    randomized Controlled Trial
    false
    blinding
    not-confirmed
    peer Reviewed
    true
    basis
    Analytical and numerical theory of interacting anyons. No human randomized controlled trial is reported.
    sources

    https://www.nature.com/articles/nphys1396

    review Scope
    Existing publication-specific assessments and bibliographic indexing; no blanket full-text appraisal.
    assessed At
    2026-10-27
    study Design Assessment
    is Randomized Controlled Trial
    false
    blinding
    Not applicable to a clinical-trial grade
    basis
    Analytical and numerical theory of interacting anyons. No human randomized controlled trial is reported.
    sources

    https://www.nature.com/articles/nphys1396

    category
    peer-reviewed
    peer Reviewed
    true
    collection
    general
    chapter Number
    10
    topic Id
    fibonacci-quantum-information
    topic Title
    Quantum information and Fibonacci dynamics
    trust Score
    1
evidence
evidence Type
Analytical and numerical theory of interacting anyons
evidence Class
mathematical_computational_model
measurement
Microscopic anyon model; exact solution and numerical spectra
measured Genes
None recorded
pathways
None recorded
relationship Note
Background literature only. This paper does not test or validate an OXTR–Fibonacci relationship.
clinical Evidence
false
review Depth
Abstract and selected source passages: Abstract; Figure 3, The Fibonacci theory; publisher metadata.
full Paper Appraisal
Not completed; review depth states the material assessed.
jadad
status
not-applicable
score
Not recorded
reason
Not a human randomized controlled trial.
condition Evidence
None recorded
conditions
None recorded
topic Trust Scores

1

full Text
status
not-indexed
retrieval Available
false

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